>From David > 12 replies to my question is not bad but the integral is actually about what > the gravity force is to a spherical mass distribution compared to a point > mass. The so called center of gravity can not be used as a center of gravity > since matter closer to a body attracts more than what the remote parts do. > How big can this effect be? > Can anyone solve the integral? I haven't even tried, yet. Can Maxima solve > it? > David
David, I must apologize as well. Guess you could say I intentionally "hijacked" your thread. In your original question you brought up interesting concepts that were related to a branch of mathematical study that I've been exploring for years. I only hope the tangential aspects of what has been discussed in your hijacked thread has been be of some interest to the readers, including you. Following up on some of the tangential aspects, the physics text books state that the force known as Gravity is considered to be several orders of magnitude weaker than the strong and weak nuclear forces. This is basic high school physics. In the meantime, David brings up an interesting concept that I consider related to a similar discussion pertaining to whether it is (legally) appropriate to computer model the effects of gravity using a point mass, or whether one should model the effect as a spherical mass distribution. From my own POV, and I'm speaking strictly from a computer programmer's POV, it is FAR more convenient in the heuristic sense to use a centralized point position in order model/generate orbital simulations based on the so-called laws of Celestial Mechanics. If one models one's algorithms using a point mass concept, it is important to "play god" and summarily change the rules so-to-speak where appropriate, particularly when the orbiting satellite approaches too close to the main orbital body. To do so introduces bizarre/chaotic orbital behavior. While it would probably be more accurate (or realistic) to employ a spherical mass distribution formula, to approach the problem as a computer programming exercise, would increase the complexity of the algorithms to the point that it would quickly become impossible to code. After reading just a sprinkle of Miles Mathis's papers, a novel concept recently dawned on me pertaining to the fact that we could speculate on the premise that the force of gravity may not necessarily be as weak as the text books have always claimed the force to be. What if we looked at the manifestation of gravity as emanating from the "center" of each sub-atomic particle, what then? What if we were to move the ground rules for "spherical mass distribution" away from the surface of typical macro bodies, like stars, planets, or moons, and scale it all the way down to the surface radius of protons and neutrons... how strong would the "point mass" force of gravity manifest at quantum-like distances? Obviously at that scale of distance the effects of gravity would be several magnitudes stronger that what is experienced within the familiar macro world! After all, we are told neutron stars are held together by the crushing force of the star's own gravity! A neutron star is essentially a gazillion sub-atomic "point mass" neutron particles collectively behaving as if they were all just one massive spherical mass distribution set as perceived on the macro scale. I suspect that in some of Miles Mathis' paper he is hinting at something akin to this. I suspect Miles is also hinting at the premise that gravity, just like all the other forces, are essentially one and the same "force" manifesting in different ways and/or scales of distance. Regards, Steven Vincent Johnson www.Orionworks.com www.zazzle.com/orionworks
